Monte Carlo Simulation

 

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In this page you can find references (books and websites)

and example (with some source codes) about Monte Carlo Simulation.

 

"Anyone who considers arithmetical methods of producing random digits is, of sourse, in state of sin."

-John von Neumann, 1951

"Anyone who as not seen the above quotation in at least 100 places is probably not very old."

-D.V.Pryor, 1993

 

What I'm talking about

The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling
experiments on a computer. The method applies to problems with no probabilistic content as well as to those with inherent probabilistic
structure. Among all numerical methods that rely on N-point evaluations in M-dimensional space to produce an approximate solution, the
Monte Carlo method has absolute error of estimate that decreases as N superscript -1/2 whereas, in the absence of exploitable special
structure all others have errors that decrease as N superscript -1/M at best.

Examples

a Good exencise :
Source fortran 77 code simulating the equlibrium configuration of n-megnetics dipoles in a 2D system (XY) in a uniform magnetic ortogonal to the XY plane. If the code isn't clearly explaned, please contact me.
NOTE1 : file dm.dip is the connectivity matrix of dipoles. (element i,j is the distance between                dipole n°i and dipole n°j).
NOTE2 : file ns.dip is the file of coordinates in the format x,y.

View the Source Code (html format)

- Shell Model the Monte Carlo Way

- Semi-Classical Partition Function

- An Exercise

Monte Carlo Methods (University of Tennessee page)
- MC Example from Anthony Sun Home Page "A firm that sells product X under a pure/perfect competition market wants to know the probability distribution for the profit of this product and the probability that the firm will loss money when marketing it. "
- The Monte Carlo Method to approximate Pi

Links

- History of Monte Carlo Methods
- Standard Deviation and Mean
- Lotto number generator
- Playing card probability
- Normal distribution random number generator
- Monte Carlo Integration
- Black-Scholes option pricing model
- Binomial option pricing model
- Portfolio optimization
- Multiple regression
- Bootstrap - a non-parametric approach
- Multivariate probability distribution
Usefull utilities for Random Numbers, Statistical Distribution Function in VBA (Visual Basic for Application) from Anthony Sun Home Page
- RANDOM NUMBER GENERATORS (from University of Salzburg)
- TESTS FOR RANDOM NUMBERS (from University of Salzburg)
- LINKS (from University of Salzburg)
A Server on the Theory and Practice of Random Number Generation

(from University of Salzburg)

Documentation, Software, News & Workshops

- NEWS IN THE FIELD (from University of Salzburg)  - LITERATURE (from University of Salzburg)  - SOFTWARE (from University of Salzburg)
THE WWW VIRTUAL LIBRARY: RANDOM NUMBERS and MONTE CARLO METHODS
Discussion List - unmoderated on-line discussions   &   Conferences
Worldwide Simulation Course Links          Welcome To The Simulation Education HomePage
Relevant Links (GO THERE)
SPECIALISTS IN RANDOM NUMBER GENERATION AND (QUASI) MONTE CARLO METHODS
Monte Carlo Surface to Surface Particle Transport (On line Book)
Simulation News Europe (abbreviated SNE) publishes information related to modelling
and simulation
Some Monte Carlo Books i found at Amazon.com (Plenty of other titles)
Markov Chain Monte Carlo in Practice
W. R. Gilks(Editor), et al / Hardcover / Published 1996
Our Price: $79.95
Monte Carlo : Concepts, Algorithms, and Applications (Springer Series in Operations Research)
George S. Fishman / Hardcover / Published 1996
Our Price: $69.95
Monte Carlo Methods : Basics (Vol 1) Vol 1
Malvin H. Kalos, Paula A. Whitlock (Contributor) / Paperback / Published 1986
Our Price: $105.00
Monte Carlo Simulation in Statistical Physics : An Introduction (Springer Series in Solid-State Sciences, 80)
K. Binder, D. W. Heermann / Paperback / Published 1998
Our Price: $24.95

The Coimbra School on Computational Physics

Click Here

The Coimbra School Text & Notes

 

Pasquali Home Page MC simulation of a CdTe thin films growing process Motion of Electron in Ionized Gases Parma Physics Department